Discovering Model Structure of Dynamical Systems with Combinatorial Bayesian Optimization
Authors: Lucas Rath, Alexander von Rohr, Andreas Schultze, Sebastian Trimpe, Burkhard Corves
TMLR 2024 | Venue PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | We empirically evaluate the method on symbolic benchmark problems for equation discovery of nonlinear dynamical systems (Brunton et al., 2016; Mangan et al., 2017). We extend these benchmarks to include inequality constraints in the form of Lasso regularization to combat overfitting, and consider crash constraints tackling numerical instabilities and failures. As a real-world application example, we further optimize a knowledge-driven formulation of a multibody driving simulation model. |
| Researcher Affiliation | Collaboration | Lucas Rath EMAIL Institute for Mechanism Theory, Machine Dynamics and Robotics, RWTH Aachen University BMW AG Alexander von Rohr EMAIL Institute for Data Science in Mechanical Engineering, RWTH Aachen University Andreas Schultze EMAIL BMW AG Sebastian Trimpe EMAIL Institute for Data Science in Mechanical Engineering, RWTH Aachen University Burkhard Corves EMAIL Institute for Mechanism Theory, Machine Dynamics and Robotics, RWTH Aachen University |
| Pseudocode | Yes | Algorithm 1 Simulated annealing for categorical variables; Algorithm 2 Bayesian Optimization for Model Structure Selection |
| Open Source Code | Yes | The code for the optimizer and the benchmark problems are publicly available at https://github.com/lucasrm25/Model-Structure-Selection-CBOSS |
| Open Datasets | Yes | We use some of the benchmark problems and a similar learning setup from Brunton et al. (2016); Mangan et al. (2017).; Table 3: Benchmark problem parameters |
| Dataset Splits | No | The paper states: "The available noisy measurements for parameter estimation and model evaluation consists of a single simulation run, starting at an initial state x(t0 = 0), simulated with a fixed simulation time step size t up to the stop time tf." This describes the data generation but does not provide explicit training/test/validation splits. |
| Hardware Specification | Yes | The benchmark experiments ran on Intel Xeon Platinum 8160 Processors Sky Lake at 2.1 GHz, on 4 isolated physical cores. The optimization and the simulations of the multibody dynamical problem were performed on a 2x Intel Xeon Gold 6256 3.6Hz computer, running a Red Hawk Linux RTOS (by Concurrent Real-Time). The first 12 cores were dedicated to the optimizer, while the remaining 12 cores of the second CPU socket were shielded and dedicated to simulations. |
| Software Dependencies | No | The paper mentions "Simpack1 simulation software" but does not provide a specific version number. It also mentions "Red Hawk Linux RTOS (by Concurrent Real-Time)" which is an operating system, not an ancillary software dependency with a version for the implementation of the core methodology. No other software libraries or packages with version numbers are specified. |
| Experiment Setup | Yes | Table 2: Optimizer hyperparameters used for all experiments. The upper-script (0) denotes the initial value used for hyperparameter optimization. In CBOSS, we use the same regression hyperparameters to learn the objective and inequality constraint functions. (Examples include: CBOSS T P regression : σ2 m hyperprior Equation 7 σ2 m Γ(2, 15), σ2 (0) m = 0.15; CBOSS AF exponents Equation 18 βfeas = 20, βsucc = 5; CBOSS AF optimizer : SA max. iterations Algorithm 1 N = 100) |